- What is the binary system?
- How does the binary system work?
- Characteristics of the binary system
- Applications of the binary system
- Solved problems of binary code
We explain what the binary system is, how it works, its applications and other characteristics. Also, solved exercises.
What is the binary system?
The binary system or dyadic system is a fundamental numbering system in the computing and computing, in which the totality of the numbers can be represented using figures composed of combinations of only two digits.
In the case of binary code, the digits used are zeros and ones. We must not confuse the system with the code, since the first one could operate with digits like a and b (since the logic is the same), while the second operates specifically with 1 and 0.
The binary code is fundamental for the construction of the computers that we know today, especially because it adapts well to the presence or absence of voltages electrical, thus giving rise to a bit from information: present or absent, that is, 1 or 0, respectively.
However, binary code was not invented exclusively for the computer world. Already in Eastern antiquity many mathematicians such as the Hindu Pingala (c. III or IV century BC) had proposed it, coinciding in many cases with the invention of the number 0.
In fact, oracle books such as the I Ching are composed based on their own code, ordering their hexagrams in series equivalent to 3 "bits”. Later, the Chinese philosopher Shao Yong (1011-1077) ordered them according to a binary method.
For its part, the modern binary system was the work of the German philosopher Gottfried W. Leibniz (1646-1716). Later, in 1854, the British mathematician George Boole (1815-1864), detailed the Boolean Algebra, fundamental in the development of the current binary system in electronic circuits.
The first attempts to put this system into practice were the work of the Americans Claude Shannon (1916-2001) and George Stibitz (1904-1995) in 1937.
How does the binary system work?
The binary system works based on the representation of any information by two figures. In binary code they are 0 and 1, but they could well be anything, as long as they are the same and represent the same thing: a binary opposition, such as yes or no, up or down, on or off.
In this way, this code allows information to be “written” through similar physical elements: the polarity of a magnetic disk (positive or negative), the presence or absence of electrical voltage, etc.
Therefore, the binary system allows any letter or decimal value to be "translated" into a binary sequence, and it even allows arithmetic and other types of operations.
For example, the letter A in binary code is represented by 1010, while the number 1 is represented by 0001. In other codes, that same information could be represented binary as abab Y bbba, or +*+* Y ***+, for example.
Thus, according to the binary code, the word etcetera would be represented like this:
01100101 (e)
01110100 (t)
01100011 (c)
11000011 (e)
10101001 (´)
01110100 (t)
01100101 (e)
01110010 (r)
01100001 (a)
Characteristics of the binary system
The binary system is characterized by the following:
- It uses any two units (1 and 0 in the case of binary code) to represent specific information through specific sequences of those digits. They must always be two, of totally distinguishable and mutually exclusive values (there cannot be 1 and 0 at the same time).
- Represents the basis of computer and computational systems, in which a sequence of eight bits constitutes a byte of information, corresponding to a letter, number or character.
- It allows translating any data expressed in decimal, hexadecimal or octal notation, among other information notation systems (ASCII, etc.).
- It allows the reading of real conditions and materials whose physical states can be one or the other: magnetic polarity, voltage, etc.
Applications of the binary system
The binary system allows numerous current uses, for example:
- Schedule of microprocessors.
- Encryption of confidential information.
- Transfer of data from one computer system to another.
- Protocols computer digital communication.
Solved problems of binary code
Go from decimal system to binary system:
23 = 10111
17 = 10001
20 = 10100
Go from binary system to decimal system:
1111 = 15
10110 = 22
10000 = 16